Spot on. ISO is basically amplification, and if you're amplifying noise then you get more noise. It's the situations that put you in high ISO the cause the IQ degradation. One factor that hasn't been mentioned about high-ISO IQ in general is that dim light is generally poor quality light; it's not just a dimmer version of good light. Due to the nature of various light sources, including the sun, dimmer light often is missing components of the spectrum. Then you amplify this with ISO and you wonder why the exposure is right but it still looks wrong. Custom WB is my friend here! If you're shooting in low light, get familiar with shooting a WB sample. Expose a clean white surface down to gray and then select that in-camera as a custom WB. I think you can do it the other way also, selecting it and then shooting. Sure a gray card is better but finding a good white thing is way easier. Just be careful that you're not shooting a white paint that has a slight tint to it, as whites often do. White plastic cooler, white jersey, white wall that looks like it's really white, or even a gray thing. You just want it to be neutral.
As for manual, I used to shoot Av a lot but for sports (nearly all of my shooting) I'm generally locking the aperture and shutter down so it's either Auto-ISO or manual ISO. Auto is great when players are running through shadows, but for an evenly lit scene (hazy day is perfect) I'll go manual so I can batch-correct exposure later if I want. When you'e displaying a bunch of photos at once, you want them looking the same.
